A fast FFT-based discrete Legendre transform

被引：10

作者：

Hale, Nicholas ^{[1
]}

Townsend, Alex ^{[2
]}

机构：

[1] Univ Stellenbosch, Dept Math Sci Appl Math, ZA-7600 Stellenbosch, South Africa

[2] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2016年 / 36卷 / 04期

基金：

美国国家科学基金会;

关键词：

discrete Legendre transform; Legendre polynomials; Chebyshev polynomials; fast Fourier transform; FAST FOURIER-TRANSFORMS; GEGENBAUER POLYNOMIALS; NONEQUISPACED DATA; FAST ALGORITHMS; COMPUTATION; EXPANSIONS; QUADRATURE; NODES;

D O I：

10.1093/imanum/drv060

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An O(N(log N)(2)/log log N) algorithm for the computation of the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equally spaced points in the frequency domain. Both components are based on the fast Fourier transform, and as an intermediate step we obtain an O(N log N) algorithm for evaluating a degree-(N - 1) Chebyshev expansion on an N-point Legendre grid. Numerical results are given to demonstrate performance and accuracy.

引用

页码：1670 / 1684

页数：15

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